Statistics and Psychology

Definition of Statistics:

Statistics is science of classifying, summarizing, organizing and analyzing data.

Main Division of Statistics:

The two main divisions of statistics are:

 Descriptive statistics

 Inferential statistics

 Descriptive Statistics:

 Definition:

The techniques of descriptive statistics allows us to organize, summarize and analyze observations so that they become easier to understand.

Two main types:

MEASURES OF CENTRAL TENDENCY (mode/median/mean)

MEASURES OF VARIABILITY/SPREAD (range/variance/SD)

It also includes

• Frequency distribution: Organizing data, Histogram, Frequency Polygon and Graphical representations of the data

• Descriptive Statistics are used to describe the data

• It is first step in any statistical analysis

 Inferential Statistics:

Techniques in inferential statistics are used to draw inferences about conditions that exist in population from the study of a sample.

Types:

Hypothesis testing: Null and alternative hypothesis, level of significance, degree of freedom, directional and non directional test, types of error.

• Single sample hypothesis testing

Z-test

one sample t-test

paired sample t-test

• Hypothesis testing with two independent sample

Independent sample T-test

Analysis of variance(ANOVA)

Chi square test

Correlation

Regression

Description of Basic terms used in Statistics:

Organizing data: The word 'Data' is plural for 'datum'; datum means facts. Statistically the term is used for numerical facts such as measures of height, weight and scores on achievement and intelligence tests.

Tests, experiments and surveys in education and psychology provide us valuable data, mostly in the shape of numerical scores. For understanding data available and deriving meaning and useful conclusion, the data have to be organized or arranged in some systematic way. This can be done by following ways:

1. statistical tables

2. rank order

3. frequency distribution

Grouped data: Data which have been arranged in groups or classes rather than showing all the original figures. grouped data are presented in the form of a frequency distribution table.

Graphical representation of data: Histogram, Frequency Polygon, Pie Diagram

Range: The "range" is just the difference between the largest and smallest values.

Class width: Difference between the two boundaries of a class.

Population: Group of observations about which investigator wishes to draw conclusion

Sample: Part of Population

Random Sampling: A technique through which each possible sample of equal size has equal probability of being selected from the population

Variable: A characteristic that may take on different values.

Constants: A characteristic that remain the same.

Scales of Measurement: Nominal scale, Ordinal Scale, interval scale and Ratio Scale.

Descriptive Statistics: The techniques of descriptive statististics allows us to organize, summarize and analyze observations so that they become easier

to understand.

Inferential Statistics: Techniques in inferential statistics are used to draw inferences about conditions that exist in population from the study of a sample.

Mean: average

Mode: most frequently occurring score

Median: middle score in rank order

Range: Highest score in a set of numbers minus the lowest score

Variance: The mean squared deviation from the mean

Standard Deviation: Tells us how much the scores deviate, on average, from the mean of all scores

Z score Standard deviation units -- tells us how far a score deviates from the mean of its distribution

Probability: A probability provides a quantitative description of the likely occurrence of a particular event. Probability is conventionally expressed on a scale from 0 to 1; a rare event has a probability close to 0, a very common event has a probability close to 1

Hypothesis Testing: A process by which an analyst tests a statistical hypothesis.

The methodology employed by the analyst depends on the nature of the data used, and the goals of the analysis.

The goal is to either accept or reject the null hypothesis.

Importance, Application and Limitation of Statistics in Psychology.

• Statistics the most important science in psychology as well as in all fields because

it only gives the results of our experiences.

• Statistics provides simple yet instant information on the matter it centers on.

• Provides a vivid presentation of collected and organized data through the use of figures, charts, diagrams and graph

• Raw data has little use if it cannot be synthesized into a larger overall picture

Summaries provided by statistics create meaning from aggregate data that can be used to help people to live more fulfilling and powerful lives.

• Through statistics, psychologists want to learn to select an appropriate statistical test to make research conclusion/make decisions.

• In psychology statistics used to develop and test theories of human behavior

• Statistical methods are useful tools in aiding researches

• Helps in providing the government more information about its citizens.

• Statistical results may initiate social reforms that would help benefit the standard of living 

• Aids in knowing which problems or matters are there to prioritize and give much attention to.

Much of psychological research involves measuring observations of particular characteristics of either a population, or a sample taken from a population. These measurements yield a set of values or scores, and this set represents the findings of

the research, or  data. Often, it is impractical to completely measure the  characteristics of a given population, known as  parameters, directly. Thus,  psychologists often focus on the characteristics of samples taken from a population. These characteristics are called statistics.  The psychologist then uses these sample statistics to make inferences about population parameters.

- Using statistics the hypotheses can be tested,

leading the therapist to better methods of intervention & evaluation.

- Using statistics we can collect data in an unbiased (as possible) manner

- It analyze observations

- Determine if a change has occurred or not and to what extent

- Draw logical conclusions from the results to inform further research and understanding

- Statistics provides procedures for the organization and analysis of data.

Psychologists often use both descriptive statistics and inferential statistics.

Various measurement scales are used to categorize statistical data into meaningful and comparable form.

• Nominal scales.
• Ordinal scales.
• Interval scales
• Ratio scales.
• Continuous and discontinuous scales.

Descriptive statistics employs a set of procedures that make it possible to meaningfully and accurately

 Summarize and describe samples of data.

Organization of data.

            A frequency distribution,

            Frequency polygons

Measures of central tendency

            Mean

            Median

            Mode

Measures of variation

            Range

            Variance

            standard deviation

Inferential statistics involves mathematical procedures that allow psychologists to

 make inferences about collected data. For example, these procedures might be used to:

- estimate the likelihood that the collected data occurred by chance (that is, to make probability predictions)

- to draw conclusions about a larger population from which samples were collected

 The procedures are usually used to test hypotheses and establish probability.

Some of the more commonly used statistical tests in psychology are:

Parametric tests

Student's t-test

analysis of variance (ANOVA)

ANCOVA (Analysis of Covariance)

MANOVA (Multivariate Analysis of Variance)

regression analysis

linear regression

hierarchical linear modelling

correlation

Pearson product-moment correlation coefficient

Spearman's rank correlation coefficient

Non-parametric tests

chi-square

Mann–Whitney U

Limitation Os Statistics in Psychology:

 Statistics does not study qualitative phenomena:

Statistics deals with facts and figures. So the quality aspect of a variable or the subjective

phenomenon falls out of the scope of statistics. For example, qualities like beauty, honesty, intelligence etc. cannot be numerically expressed. So these characteristics cannot be examined statistically.

 Statistics does not study individuals:

Statistics deals with aggregate of facts. Single or isolated figures are not statistics.

This is considered to be a major handicap of statistics.

Statistics can be misused:

Statistics is mostly a tool of analysis. Statistical techniques are used to analyze and interpret the collected information in an enquiry. As it is, statistics does not prove or disprove anything. It is just a means to an end. Statements supported by statistics are more appealing and are commonly believed. For this, statistics is often misused. Statistical methods rightly used are beneficial but if misused these become harmful. Statistical methods used by less expert hands will lead to inaccurate results. Here the fault does not lie with the subject of statistics but with the person who makes wrong use of it.

Purposive misuses:

 The most total limitation of statistics is that its purposive misuse. Very often erroneous information may be collected. But sometimes some institutions use statistics for self interest and puzzling other organizations.